Solve for $x$ and $y$ using elimination. ${3x-3y = -12}$ ${-2x+3y = 17}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {3x-3y = -12}\thinspace$ to find $y$ ${3}{(5)}{ - 3y = -12}$ $15-3y = -12$ $15{-15} - 3y = -12{-15}$ $-3y = -27$ $\dfrac{-3y}{{-3}} = \dfrac{-27}{{-3}}$ ${y = 9}$ You can also plug ${x = 5}$ into $\thinspace {-2x+3y = 17}\thinspace$ and get the same answer for $y$ : ${-2}{(5)}{ + 3y = 17}$ ${y = 9}$